Fuzzy-approximation-based global adaptive control for uncertain strict-feedback systems with a priori known tracking accuracy

Abstract

In this study, we propose a novel adaptive backstepping fuzzy control scheme for a class of uncertain strict-feedback systems where the tracking accuracy is known a priori, and we also introduce a multiswitching-based adaptive fuzzy controller. Compared with the existing method for adaptive fuzzy control, the advantages of the proposed scheme are as follows. First, the controller guarantees that all the closed-loop signals are globally uniformly ultimately bounded, which differs from most existing adaptive fuzzy control approaches where the semi-global boundedness of the closed-loop signals is ensured under a harsh assumption on the approximation domain of the fuzzy logic system. Second, our controller ensures that the tracking error converges to an accuracy that is given a priori for the uncertain strict-feedback system, which cannot be achieved using existing adaptive fuzzy control methods. Third, based on some nonnegative functions, we analyze the convergence of the tracking error using Barbalat's Lemma. Fourth, the main technical novelty is the construction of three new nth-order continuously differentiable switching functions, which are used to design the desired controller. Finally, three simulation examples are provided that illustrate the effectiveness of the proposed control strategy.